Space and time dilation

If space is the absence of mass-energy (which are absolute), then how do we know it exists physically (with no observer)? Also is it possible that time does not dilate (isn't time invariant by definition?) but the clocks slow down due to energy conservation principles at work?

It is philosophical. The philosophy of space-time goes back to Gottfried Leibniz. Can physical space exist separately from matter? If the answer is no then the relative is abstract and depends on the absolute.

Mach's view was that space is non existent by itself - it is only what lies inbetween the matter - Einstein believed you could have a totally empty universe, and write equations that predicted things about space even though you regarded space as empty of matter. But that is only an if proposition - in reality all evidence points to the fact that while space may not be made out of chucks of matter, it is nonetheless a plenum of activity - it has many measurable properties like inductance , capacitance, and impedance, and some local property that is most likely the origin of inertia - this was one of the characteristics Einstein dwelled upon - as opposed to the ideas of Mach. As Democrities opined - it is only the atoms and the void that is real - and perhaps, in reality, the universe may be even less substantive - maybe it is only the void that is real.

Einstein's equations allow the possibility of time dilation and time travel, which is a contradiction because time is an invariant by definition. There is no dynamics in the time axis, otherwise nothing could move and we get a block universe.

Einstein's equations allow the possibility of time dilation and time travel, which is a contradiction because time is an invariant by definition. There is no dynamics in the time axis, otherwise nothing could move and we get a block universe.

What does "dynamics in the time axis" mean? And why do you think we aren't in a block universe? (for background on the block universe/block time concept, see this Scientific American article by physicist Paul Davies)

Einstein's equations allow the possibility of time dilation and time travel, which is a contradiction because time is an invariant by definition. There is no dynamics in the time axis, otherwise nothing could move and we get a block universe.

General relativity allows movement in space, not in spacetime.

Time travel is absolutely possible. I've traveled seven days since last week! :)

Also, not only do Einstein's equations allow the possibility of time dilation, time dilation is routinely shown to exist experimentally. Time dilation is one of the better established parts of relativity theory actually.

I join the others in questioning where you get your definition of time being invariant. Defined as it is in physical laws, time passes at different rates depending on the relative motions of the time observers.

There certainly is room, in the classical picture of GR, at least, to call all of 4-D time space a pre-determined set piece. Free will is not necessary to the classical theory. Fate is entirely consistent with it. But, quantum mechanics does not necessarily agree on that point and many people think that there is an underying quantum mechanical explanation of GR.

Consider this excerpt from Einsteins Leyden address:
...There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space... http://www.europhysicsnews.com/full/27/article4/article4.html

Does this mean space cannot exist without matter? Not entirely. Under the equivalence principle, space could still exist in a universe that consisted solely of energy. But such a universe would probably be unstable and suffer a cataclysmic transition event, such as a big bang.

In simple terms, relativity is a four dimensional pythagom's theorem. Time is one leg of that hypertriange, hence cannot be invariant.